Currently, the laser interferometry is applied to detect GW.
The typical laser interferometer is equal-arm Michelson consisting of four laser links.
The equal-arm Michelson has been employed for ground-based GW detectors [1]}, [2]}, where the laser noise experiences the same delays in the links and hence cancels.
Unlike ground-based GW detectors, space-borne GW detectors have unequal armlengths due to the movement of satellites [3]}, [4]}.
Thus, it is hardly to construct an equal-arm Michelson for space-borne GW detectors, and the laser noise will dominate the detector noise [5]}.
To cancel the laser noise in the unequal-arm detectors, Tinto et.al [6]}, [7]} proposed the TDI technique adopting specific combinations of laser links.
Among all possible TDI combinations, the TDI channel \(\rm A\) , \(\rm E\)  and \(\rm T\)  are the most commonly used, and they form the orthogonal channel group \(\rm AET\) .
In the GW detection, \(\rm A/E\)  channels are sensitive to GW, while \(\rm T\)  channel works effectively for monitoring the detector noise.
